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TECHNICAL PAPERS

Explicit Modal Analysis of an Axially Loaded Timoshenko Beam With Bending-Torsion Coupling

[+] Author and Article Information
J. R. Banerjee

Department of Mechanical Engineering and Aeronautics, City University, Northampton Square, London EC1V OHB, UK

J. Appl. Mech 67(2), 307-313 (Nov 08, 1999) (7 pages) doi:10.1115/1.1303984 History: Received November 03, 1998; Revised November 08, 1999
Copyright © 2000 by ASME
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References

Timoshenko, S. P., Young, D. H., and Weaver, W., 1974, Vibration Problems in Engineering, 4th Ed., Wiley, New York.
Thomson, W. T., 1983, Theory of Vibration and Application, 2nd Ed., George Allen and Unwin, London.
Tse, F. S., Morse, I. E., and Hinkle, R. T., 1978, Mechanical Vibrations: Theory and Applications, 2nd Ed., Allyn and Bacon Inc., London.
Horr,  A. M., and Schmidt,  L. C., 1995, “Closed-Form Solution for the Timoshenko Beam Theory using a Computer-Based Mathematical Package,” Comput. Struct., 55, No. 3, pp. 405–412.
White,  M. W. D., and Heppler,  G. R., 1995, “Vibration Modes and Frequencies of Timoshenko Beams With Attached Rigid Bodies,” ASME J. Appl. Mech., 62, No. 1, pp. 193–199.
Farchaly,  S. H., and Shebl,  M. G., 1995, “Exact Frequency and Mode Shape Formulae, for Studying Vibration and Stability of Timoshenko Beam System,” J. Sound Vib., 180, No. 2, pp. 205–227.
Friberg,  P. O., 1983, “Coupled Vibration of Beams—An Exact Dynamic Element Stiffness Matrix,” Int. J. Numer. Methods Eng., 19, No. 4, pp. 479–493.
Friberg,  P. O., 1985, “Beam Element Matrices Derived from Vlasov’s Theory of Open Thin-Walled Elastic Beams,” Int. J. Numer. Methods Eng., 21, No. 7, pp. 1205–1228.
Dokumaci,  E., 1987, “An exact Solution for Coupled Bending and Torsion Vibrations of Uniform Beams Having Single Cross-Sectional Symmetry,” J. Sound Vib., 119, No. 3, pp. 443–449.
Banerjee,  J. R., 1989, “Coupled Bending-Torsional Dynamic Stiffness Matrix for Beam Elements,” Int. J. Numer. Methods Eng., 28, No. 6, pp. 1283–1298.
Banerjee,  J. R., and Fisher,  S., 1992, “Coupled Bending-Torsional Dynamic Stiffness Matrix for Axially Loaded Beam Elements,” Int. J. Numer. Methods Eng., 33, No. 6, pp. 739–751.
Banerjee,  J. R., and Williams,  F. W., 1992, “Coupled Bending-Torsional Dynamic Stiffness Matrix for Timoshenko Beam Elements,” Comput. Struct., 42, No. 3, pp. 301–310.
Banerjee,  J. R., and Williams,  F. W., 1994, “Coupled Bending-Torsional Dynamic Stiffness Matrix of an Axially Loaded Timoshenko Beam Element,” Int. J. Solids Struct., 31, No. 6, pp. 749–762.
Bercin,  A. N., and Tanaka,  M., 1997, “Coupled Flexural-Torsional Vibrations of Timoshenko Beams,” J. Sound Vib., 207, No. 1, pp. 47–59.
Rayna, G., 1986, REDUCE Software for Algebraic Computation, Springer-Verlag, New York.

Figures

Grahic Jump Location
Coordinate system and notation for an axially loaded bending-torsion coupled Timoshenko beam
Grahic Jump Location
(a) Variation of Δ with frequency (ω) for the case when p2=r2=s2=0; (b) variation of Δ with frequency (ω) for the case when p2=0.1886,r2=0.000447, and s2=0.00233; (c) variation of Δ with frequency (ω) for the case when p2=−0.1886,r2=0.000447, and s2=0.00233
Grahic Jump Location
The first four natural frequencies and mode shapes of an axially loaded bending-torsion coupled Timoshenko beam (813) with cantilever end condition for the case when p2=0.1886,r2=0.000447, and s2=0.00233

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